A photographic technique known as dual photography, which exploits Helmholtz reciprocity, allows for the position of a digital camera and a digital light source to be mathematically interchanged. This mathematical interchange was originally developed to aid in the rendering of computer generated scenes and enabled the scene to be “viewed” from the position of the original light source a though “illuminated” from the position of the original camera. An original purpose of this methodology was to show how dual photography could be used to capture and relight scenes. Subsequent work concentrated on the creation of adaptive and non-adaptive algorithms to more efficiently capture the large amounts data necessary to build the light transport matrices require for the technique to work. Because the original goal of dual photography was the rendering and relighting of computer generated scenes, no attempt was made to recover details from the scene not directly visible to either the camera or the digitized light source. Additionally, no work has been performed related to describing the quality of the dual image. Neither of these oversights effected the exploitation of dual photography for the original intended purposes. Nevertheless, for applications outside the computer graphics community, the recovery of scene information not directly visible to either the camera or the light source and a metric of the quality of the dual image may be of considerable interest.
In one of the configurations used to demonstrate the dual photography methodology, a playing card was positioned such that the face of the playing card was not visible to a camera. A pixilated light source, projector, was placed with a full view of the face of the playing card and a book was placed so that when a pixel illuminated the playing card, reflections from the card could be imaged by the camera after an intermediary reflection from the book.
The pixels of the projector individually illuminated the playing card and the subsequent reflections from the card onto the book were imaged by the camera. Using Helmholtz reciprocity to mathematically interchange a digital light source and a camera as know in the art, the projector was converted to a “virtual camera” and the face of the playing card was revealed to be the King of Hearts.
While the technique of dual photography is effective for its original purpose, for most applications outside the field of computer generated graphics, there is no reason to attempt dual photography as described above. If it is possible to place a pixilated light source in a position to directly view the object of interest, it is much easier to position a camera in that position and image the object directly instead of going through the complicated and data intensive process of creating a dual image. There are, however, many applications where discretely viewing an object hidden from direct view of a camera may be of interest. Extending the concept of dual photography into one of indirect photography, where neither the camera nor the controlling light source has a direct line-of-sight to the object of interest would open up countless new opportunities in the field of remote sensing and the other fields of study.
Therefore, there is a need in the art for a photographic methodology which allows for the relief of the line-of-sight requirement and while still capturing scene information not previously available to be recovered.